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Frederick Kingdom; Mach Bands: Contrast normalization?. Journal of Vision 2013;13(9):1146. doi: 10.1167/13.9.1146.
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© ARVO (1962-2015); The Authors (2016-present)
Aim. Mach bands are the illusory bright and dark bars seen at the knees and feet of luminance trapezoids. The most popular account of Mach bands is that they result from a feature coding process that generates a sparse, binary representation of luminance discontinuities in terms of ‘edges’ and ‘bars’. According to this account, the feet and knees of trapezoids elicit relatively strong responses in even-symmetric filters, and these are interpreted as indicative of bars. The filter responses to step-edges on the other hand are interpreted as indicative of edges not bars, predicting correctly no Mach bands at step-edges. Here I show through a modelling exercise that a simpler and more parsimonious explanation of Mach bands suffices that is in keeping with recent multi-scale filtering models of brightness coding: Mach bands result from contrast normalization. Method. One-dimensional representations of stimuli were convolved with a bank of one-dimensional, 2[sup]nd[/sup]-Derivative-of-Gaussian filters that formed a complete basis set. Each convolution response was multiplied by 1/(1+kAs), where As is the amplitude response of each scale (s) of filter, and k is a factor that determines the amount of contrast normalization, set to unity for all filters and all stimuli. Filter responses were then summed to produce a predicted brightness profile. Results. Mach bands were observed in trapezoids, and Generalized Gaussian edges with exponents >1. Mach bands were not observed in step-edges, Hilbert-transformed trapezoids, trapezoids in which all phases were set to 90deg, and Generalized Gaussian edges with exponents <=1. All results are in line with psychophysical observation. Conclusion. Mach bands are caused by contrast normalization, not feature coding.
Meeting abstract presented at VSS 2013
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